b
(b)The given shape is equivalent to the following diagram The field at \(O\) due to straight part of conductor is \({B_1} = \frac{{{\mu _o}}}{{4\pi }}.\frac{{2i}}{r}  \odot \). The field at \(O\) due to circular coil is \({B_2} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi i}}{r} \otimes \). Both fields will act in the opposite direction, hence the total field at \(O\). i.e. \(B = {B_2} - {B_1} = \left( {\frac{{{\mu _o}}}{{4\pi }}} \right) \times (\pi - 1)\frac{{2i}}{r} = \frac{{{\mu _o}}}{{4\pi }}.\frac{{2i}}{r}(\pi - 1)\)